I would recommend that anyone with a genuine interest read the Bugliosi book "Reclaiming History." It is a massive tome as would be expected in setting out the case against Oswald and debunking each of the conspiracy theories. Badge man (a coke bottle in a blurry photo), mysterious deaths (not only did the majority on these lists die completely natural deaths, but if theorists believe conspirators murdered these people to silence them, why would they wait so long to do it? In some cases over 20 years), LBJ, Cubans etc are knocked down one by one in excruciating detail.
"...the principal frailities in the thinking processes of the theorists is that they rarely ever carry their suspicions, which are based on some discrepancy, anomaly, or contradiction they find, to their logical conclusion. If they did, they'd see the reductio ad adsurdum of their position. But for them, if something looks suspicious, that's enough. Instead of asking, "Where does this go?" - that is, where does the discrepancy, contradiction, or whatever, lead them? - they immediately give their minds a breather and conclude that what they find is itself proof of a conspiracy (or proof Oswald is innocent). The disprepancy or contradiction is the entire story. Nothing else has to be shown or even argued."